I just came up with this system using my own system generator... it's pretty interesting because the inner four rocky planets have very eccentric orbits, and the inner three are overlapping!

The really cool thing is that if you set it to run at a timestep of 16384 (zoom it in to 4.504 AU) you can see the innermost orbit precess around the star, and the second planet's orbit also precesses a lot more slowly. I don't know if it's just chance of how the orbital orientations were initially set up (I just randomised those) but it actually seems to be pretty stable somehow - are the bodies in some kind of resonance or something? I haven't seen them collide with eachother (not after about 2000 years of simulation time at least). I would have thought that while the first planet's orbit was precessing through the second one that the chance of collision would be much higher.

I'm just running it again as I type this and I notice that planet 2 got a bit of a kick around its precession about 90 degrees around (it skipped a bit near the 2500 year mark) but carried on otherwise unaffected. But at 2900 years the second planet orbit has rotated over 180 degrees around the star and the innermost one has done a couple of full circles around the star.

Though actually, what's really weird is that the fourth planet appears to be precessing in the opposite direction to the inner three. I tried running it at a 32k timestep and the inner three planets are precessing in a clockwise manner around the star, but the fourth orbit appears to be precessing in a counter-clockwise direction! How can that be happening??

EDIT: I just checked again, and planet 4 is definitely precessing in a counter-clockwise direction around the star while the inner three planets precess in a clockwise direction.

EDIT2: - I've attached a picture of how the rocky planets all start out anyway...

Here's a screenshot of the system after 3004 years. The orbit of the first planet has completed several precessions around the star, the second one has just completed its first complete precession, and the third orbit has just rotated a few degrees clockwise. You can superimpose this over the initial image I posted above and see how things have evolved - the fourth planet is definitely precessing in the wrong direction compared to the inner three (its orbit has rotated a few degrees in a counter-clockwise direction)!

Very interesting indeed , especially the fact of counterprecession . I have no idea why a planet performs a counter precession . Maybe Tony has ? It's possible that planets change orbit as a result of a close encounter . I had the same phenomenom simulating coorbitals a while ago . About the time where the change takes place : this must be strongly related to the initial conditions . I would like to get the initial conditions which you set at random . Can you provide them ?

I would like to get the initial conditions which you set at random . Can you provide them ?

Not unless you can tell me how to find them . I just set the longitude of ascending node of the orbit, argument of perifocus, and mean anomaly for all the planets at 180 +/- 180 degrees (so they're random). I had time frozen to start with, cranked it up to 16k timestep and then started time and watched it go.

Weird, I just ran it again and the inner two planets swapped orbits around the 2700 year mark on a 16k timestep and the third planet's orbit changed too.

I started it again (making sure I didn't set things running til I'd accelerated time to 16k), and it's at 4700 years now and the inner two planets haven't swapped places. However, the second planet's semimajor axis has shrunk a bit (it's not that much larger than the first planet's now).

planet 3 is still precessing very slowly, and planet 4 is still precessing in the opposite direction (which is bizarre. as far as I can see something has to be negative in the precession equations and I'm not sure how that can happen! And of course the planet itself is orbiting in the same direction as the other bodies). Could this be a timestep issue somehow?

After chatting with Tony, it seems that the backward precession is down to the timestep. When I tried the system on 128, the precession of all the bodies was very different (and planet 2 got tossed out at some point. Unfortunately Excel has a limit of 65k rows so there's not much point in making the output file bigger... and it got booted out at some point after the end of the file).